You don't need a full model of every atomic interaction because all of those chaotic interactions end up averaging out. Given enough coin flips you will end up on a 50/50 split even if the individual flips are unpredictable. Given enough atomic interactions the heat will transfer in the same way every time.
Impossible, since it is chaotic.
But a T(t) model should not be too hard for an LLM with a basic heat transfer book in its training set.